Method and apparatus for deghosting seismic data

ABSTRACT

Apparatus, computer instructions and method for deghosting seismic data related to a subsurface of a body of water. The method includes inputting data recorded by detectors that are towed by a vessel, the data being associated with waves travelling from the subsurface to the detectors; applying a migration procedure to the data to determine a first image of the subsurface; applying a mirror migration procedure to the data to determine a second image of the subsurface; joint deconvoluting the first image and the second image for deghosting a reflectivity of the subsurface; and generating a final image of the subsurface based on the deghosted reflectivity of the joint deconvoluting step.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of application Ser. No. 13/871,326,filed on Apr. 26, 2013, which is a Continuation of co-pendingapplication Ser. No. 13/155,778, filed on Jun. 8, 2011, which claimspriority under 35 U.S.C. §119(e) to U.S. Provisional Application No.61/393,057 filed on Oct. 14, 2010 and this application also claimspriority under 35 U.S.C. §119(a) to Patent Application No. 1054599 filedin France on Jun. 10, 2010. The entire contents of each of the abovedocuments are hereby incorporated by reference into the presentapplication.

BACKGROUND

Technical Field

Embodiments of the subject matter disclosed herein generally relate tomethods and systems and, more particularly, to mechanisms and techniquesfor deghosting seismic data.

Discussion of the Background

During the past years, the interest in developing new oil and gasproduction fields has dramatically increased. However, the availabilityof land-based production fields is limited. Thus, the industry has nowextended drilling to offshore locations, which appear to hold a vastamount of fossil fuel. Offshore drilling is an expensive process. Thus,those engaged in such a costly undertaking invest substantially ingeophysical surveys in order to more accurately decide where to drill ornot (to avoid a dry well).

Marine seismic data acquisition and processing generate a profile(image) of the geophysical structure (subsurface) under the seafloor.While this profile does not provide an accurate location for the oil andgas, it suggests, to those trained in the field, the presence or absenceof oil and/or gas. Thus, providing a high resolution image of thesubsurface is an ongoing process for the exploration of naturalresources, including, among others, oil and/or gas.

During a seismic gathering process, as shown in FIG. 1, a vessel 10drags plural detectors 12. The plural detectors 12 are disposed along acable 14. Cable 14 together with its corresponding detectors 12 aresometimes referred to by those skilled in the art as a streamer 16. Thevessel 10 may tow plural streamers 16 at the same time. The streamersmay be disposed horizontally, i.e., lying at a constant depth z₁relative to the surface 18 of the ocean. Also, the plural streamers 16may form a constant angle (i.e., the streamers may be slanted) withrespect to the surface of the ocean as disclosed in U.S. Pat. No.4,992,992, the entire content of which is incorporated herein byreference. FIG. 2 shows such a configuration in which all the detectors12 are distributed along a slanted straight line 14 that makes aconstant angle α with a reference horizontal line 30.

With reference to FIG. 1, the vessel 10 also drags a sound source 20configured to generate an acoustic wave 22 a. The acoustic wave 22 apropagates downward and penetrates the seafloor 24, eventually beingreflected by a reflecting structure 26 (reflector). The reflectedacoustic wave 22 b propagates upwardly and is detected by detector 12.For simplicity, FIG. 1 shows only two paths 22 a corresponding to theacoustic wave. However, the acoustic wave emitted by the source 20 maybe substantially a spherical wave, e.g., it propagates in all directionsstarting from the source 20. Parts of the reflected acoustic wave 22 b(primary) are recorded by the various detectors 12 (the recorded signalsare called traces) while parts of the reflected wave 22 c pass thedetectors 12 and arrive at the water surface 18. Since the interfacebetween the water and air is well approximated as a quasi-perfectreflector (i.e., the water surface acts as a mirror for the acousticwaves), the reflected wave 22 c is reflected back towards the detector12 as shown by wave 22 d in FIG. 1. Wave 22 d is normally referred to asa ghost wave because this wave is due to a spurious reflection. Theghosts are also recorded by the detector 12, but with a reverse polarityand a time lag relative to the primary wave 22 b. The degenerativeeffect that the ghost arrival has on seismic bandwidth and resolutionare known. In essence, interference between primary and ghost arrivalscauses notches, or gaps, in the frequency content recorded by thedetectors.

The traces may be used to determine the subsurface (i.e., earthstructure below surface 24) and to determine the position and presenceof reflectors 26. However, the ghosts disturb the accuracy of the finalimage of the subsurface and for at least this reason, various methodsexist for removing the ghosts, i.e., deghosting, from the results of aseismic analysis. Further, the actual measurements need to be processedfor obtaining the correct position of the various parts (reflectors) ofthe subsurface. Such a processing method is the migration.

U.S. Pat. Nos. 4,353,121 and 4,992,992, the entire content of which isincorporated herein by reference, describe processing procedures thatallow ghosts to be removed from recorded seismic data by using anacquisition device that includes a seismic streamer slanted at an angle(on the order of 2 degrees) to the surface of the water (slantedstreamer).

Using slanted streamers, it is possible to achieve ghost suppressionduring data summation operation (during pre-stack operations). In fact,the acquired data are redundant, and the processing procedure includes asummation step or “stacking” for obtaining the final image of thesubsurface structure from the redundant data. The ghost suppression isperformed in the art during the stacking step because the recordingsthat contribute to the stack, having been recorded by differentreceivers, have notches at different frequencies, such that theinformation that is missing due to the presence of a notch on oneseismic receiver is obtained from another receiver.

Further, U.S. Pat. No. 4,353,121 describes a seismic data processingprocedure based on the following known steps: (1) common depth pointcollection, (2) one-dimensional (1D) extrapolation onto a horizontalsurface, or “datuming”, (3) Normal MoveOut (NMO) correction, and (4)summation or stack.

Datuming is a processing procedure in which data from N seismicdetectors D_(n) (with positions (x_(n), z_(n)), where n=1, . . . N and Nis a natural number, x_(i)=x_(j) but z_(i) different from z_(j) with iand j taking values between 1 and N), is used to synthesize datacorresponding to seismic detectors that have the same horizontalpositions x_(n) and a same constant reference depth z₀ for all theseismic detectors.

Datuming is called 1D if it is assumed that the seismic waves propagatevertically. In that case, the procedure includes applying to eachtime-domain recording acquired by a given seismic detector a delay or astatic shift corresponding to the vertical propagation time between thetrue depth z_(n) of a detector D_(n) and the reference depth z₀.

Furthermore, U.S. Pat. No. 4,353,121 describes a summation of theprimary (primary stack) by using the NMO correction that aligns theprimaries, then a summation of the ghosts (ghost stack) by aligning theghost reflections, and then combining the results of these two steps toobtain a post-stack image with a boosted signal-to-noise ratio.

Similar to U.S. Pat. No. 4,353,121, U.S. Pat. No. 4,992,992 proposes toreconstitute from seismic data recorded with a slanted cable seismicdata as would have been recorded by a horizontal cable. However, U.S.Pat. No. 4,992,992, takes into account the non-vertical propagation ofthe seismic waves by replacing the 1D datuming step of U.S. Pat. No.4,353,121 with a 2D datuming step. The 2D datuming step takes intoaccount the fact that the propagation of the waves is not necessarilyvertical, unlike what is assumed to be the case in the 1D datuming stepproposed by U.S. Pat. No. 4,353,121.

More specifically, U.S. Pat. No. 4,992,992 reconstructs two sets ofseismic data as if they had been recorded by a horizontal streamer andthen sums the two sets after multiplication by a factor. The first setof data is synthesized by assuming that the seismic waves arepropagating upward like the primary waves, and the second set issynthesized by assuming that the seismic waves are propagating downwardlike the ghosts. Upward propagation (rising wave) is defined by anglesof propagation with respect to the horizontal between 0° and 180°, anddownward propagation (descending wave) is defined by angles ofpropagation between 180° to 360° with the horizontal.

The methods described in U.S. Pat. Nos. 4,353,121 and 4,992,992 areseismic processing procedures in one dimension and in two dimensions.Such procedures, however, cannot be generalized to three dimensions.This is so because a sampling interval of the sensors in the thirddimension is given by the separation between the streamers, on the orderof 150 m, which is much larger than the sampling interval of the sensorsalong the streamers which is on the order of 12.5 m. Also, the existingprocedures may apply a deghosting step at the beginning of theprocessing, which is not always very efficient.

Accordingly, it would be desirable to provide systems and methods thatavoid the afore-described problems and drawbacks, e.g., provide a 3Dseismic processing procedure which allows imaging of the subsurfacegeology based on marine seismic data recorded at different water depths.

SUMMARY

According to an exemplary embodiment, there is a method for deghostingseismic data related to a subsurface of a body of water. The methodincludes inputting data recorded by detectors that are towed by avessel, the data being associated with waves travelling from thesubsurface to the detectors; applying a migration procedure to the datato determine a first image of the subsurface; applying a mirrormigration procedure to the data to determine a second image of thesubsurface; joint deconvoluting the first image and the second image fordeghosting a reflectivity of the subsurface; and generating a finalimage of the subsurface based on the deghosted reflectivity of the jointdeconvoluting step.

According to still another exemplary embodiment, there is a processingdevice for deghosting seismic data related to a subsurface of a body ofwater. The processing device includes an interface configured to receivedata recorded by detectors that are towed by a vessel, the data beingassociated with waves travelling from the subsurface to the detectors;and a processor connected to the interface. The processor is configuredto apply a migration procedure to the data to determine a first image ofthe subsurface, apply a mirror migration procedure to the data todetermine a second image of the subsurface, joint deconvolute the firstimage and the second image for deghosting a reflectivity of thesubsurface, and generate a final image of the subsurface based on thedeghosted reflectivity of the joint deconvoluting step.

According to still another exemplary embodiment, there is a computerreadable medium including computer executable instructions, wherein theinstructions, when executed, implement a method for deghosting seismicdata related to a subsurface of a body of water. The method includesinputting data recorded by detectors that are towed by a vessel, thedata being associated with waves travelling from the subsurface to thedetectors; applying a migration procedure to the data to determine afirst image of the subsurface; applying a mirror migration procedure tothe data to determine a second image of the subsurface; jointdeconvoluting the first image and the second image for deghosting areflectivity of the subsurface; and generating a final image of thesubsurface based on the deghosted reflectivity of the jointdeconvoluting step.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate one or more embodiments and,together with the description, explain these embodiments. In thedrawings:

FIG. 1 is a schematic diagram of a conventional seismic data acquisitionsystem having a horizontal streamer;

FIG. 2 is a schematic diagram of a conventional seismic data acquisitionsystem having a slanted streamer;

FIG. 3 is a schematic diagram of a seismic data acquisition systemhaving a curved profile streamer;

FIG. 4 illustrates down-travelling and up-travelling waves produced by asource and recorded by plural detectors;

FIG. 5 is a flow chart of a method for generating a final image of asubsurface according to an exemplary embodiment;

FIG. 6 is a plot illustrating data processed by a migration procedure;

FIG. 7 is a plot illustrating data processed by a mirror migrationprocedure;

FIG. 8 is a plot illustrating data processed by a novel procedureaccording to an exemplary embodiment;

FIG. 9 is a flow chart illustrating a method for calculating a finalimage of a subsurface according to an exemplary embodiment;

FIG. 10 is a schematic diagram of a processing apparatus configured toperform a novel method according to an exemplary embodiment; and

FIG. 11 is a flow chart illustrating a method for deghosting accordingto an exemplary embodiment.

DETAILED DESCRIPTION

The following description of the exemplary embodiments refers to theaccompanying drawings. The same reference numbers in different drawingsidentify the same or similar elements. The following detaileddescription does not limit the invention. Instead, the scope of theinvention is defined by the appended claims. The following embodimentsare discussed, for simplicity, with regard to the terminology andstructure of migration, mirror migration and matched mirror migrationprocesses for determining a final image of a subsurface. However, theembodiments to be discussed next are not limited to these processes, butmay be applied to other processes that are used for processing seismicdata or other data related to the determination of the position of astructure that is not directly reachable for measurements.

Reference throughout the specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with an embodiment is included inat least one embodiment of the subject matter disclosed. Thus, theappearance of the phrases “in one embodiment” or “in an embodiment” invarious places throughout the specification is not necessarily referringto the same embodiment. Further, the particular features, structures orcharacteristics may be combined in any suitable manner in one or moreembodiments.

According to an exemplary embodiment, there is a method for deghostingmigration and mirror migration images by joint deconvolution forgenerating a final image of a subsurface. In another exemplaryembodiment, the deghosting is performed at the end of the processing(during an imaging phase) and not at the beginning as for thetraditional methods. In still another exemplary embodiment, no datumingstep is performed on the data. In still another exemplary embodiment,the method is applicable without restrictions as to a direction ofpropagation of the waves. According to still another exemplaryembodiment, a 3D seismic processing procedure is presented and the 3Dprocedure allows imaging of the subsurface geology based on marineseismic data recorded at different water depths. According to yetanother exemplary embodiment, the data that are processed are collectedusing streamers having a curved profile, i.e., part of the detectors arenot provided on a slanted streamer although the detectors have varyingdepths relative to the surface of the water. These kind of streamerswere disclosed in French filed Patent Application Serial No. FR1052576,entitled, Method and Device to Acquire Marine Seismic Data, the entirecontent of which is incorporated herein by reference, and also in U.S.Provisional Patent Application No. 61/392,982, entitled, Method andDevice to Acquire Seismic Data, the entire content of which isincorporated herein by reference. Also, French filed patent applicationserial no. FR1054599, having the title “Method to Process Marine SeismicData” is incorporated herein by reference.

According to another exemplary embodiment, a novel deghosting method isadapted to any broadband acquisition technique. The deghosting method isinsensitive to noise, amplitude preserving, and it is able to providethe true deghosted earth response (i.e., the response that would beobtained should the water surface be non-reflecting). Before discussingthe details of the method, an overview of the method is believed to bein order. The method produces a conventional migration as well as amirror migration, and then the method performs a joint deconvolution ofthese two images. A mirror migration is referred to as one whichmigrates from a duplicate set of receivers that are mirrored above thesurface. The process is illustrated on a 2D synthetic dataset using avelocity model with a vertical gradient, an actual airgun wavelet tomodel the shots, and a variable depth streamer. The modelling of theshots may be done with a reflecting water surface (ghosted data). Theshots with the ghost are processed through deterministic designature,migration, mirror migration, and joint deconvolution.

In the conventional migration, the primary events are perfectly stacked,while the imperfectly stacked ghost events are present in the form of acausal residual ghost wavelet (i.e., lagging the primaries). Conversely,in the mirror migration, the ghost events are perfectly stacked withtheir polarity reversed, whilst the imperfectly stacked primary eventsare present in the form of an anti-causal residual wavelet (i.e., theresidual primaries precede the well imaged ghosts).

This dual imaging of the same reflectivity with two different viewpointsis used to extract the true amplitude deghosted migration. It is areasonable assumption to consider a ghost wavelet as a minimum phasesignal, or at least a marginally minimum phase signal. Likewise it canbe considered that the mirror migration gives the same reflectivity asthe migration but distorted by a wavelet which is maximum-phase. Thiscan be considered as a binocular vision of the reflectivity with theconventional migration image colored by a normalized minimum phasedistortion, and the mirror migration image colored by a normalizedmaximum phase distortion. To recover the reflectivity in true color(i.e., without distortion) a joint minimum phase, maximum phasedeconvolution is applied on the migration and mirror migration.

Unlike conventional deconvolution, this is a well posed mathematicalproblem, which means it has a unique solution, even when the operatorshave perfect spectral notches. Therefore, there is no requirement forthe usual assumption that the reflectivity is white; the amplitudespectrum of the reflectivity remains arbitrary.

The matched mirror migration and joint deconvolution deghostingtechnique is well suited to variable depth streamer acquisition. Thetechnique is fully 3D as it makes no 2D assumptions and has nolimitations in the cross-line direction, making it suitable forwide-azimuth as well as 3D surveys.

The process of gathering marine seismic data has been discussed in U.S.Provisional Patent Application No. 61/392,982, Method and Device toAcquire Seismic Data, and thus, this process is not repeated herein.Further, the above-identified patent application identified thepossibility to gather data not only by using traditional streamers,i.e., the detectors lying along horizontal lines or along a slantedline, but also using novel streamers in which part of the detectors maylie on a curved profile (variable depths) or streamers that havemultiple slanted sections.

Such configuration is illustrated in FIG. 3, in which a streamer 52 hasa curved profile defined by three parametric quantities, z₀, s₀ andh_(c). It is noted that not the entire streamer has to have the curvedprofile. In other words, the curved profile should not be construed toalways apply to the entire length of the streamer. While this situationis possible, the exemplary embodiments do not prohibit having the curvedprofile applied to only a portion of the streamer. The first parameterz₀ indicates the depth of the first detector 54 a relative to thesurface 58 of the water. This parameter may have a value in the range ofmeters to tens of meters. For example, z₀ may be around 6 m. However, aswould be recognized by those skilled in the art, the value of z₀ dependson each application and may be related to the depth of the bottom of theocean, the depth of the reflectors, the power of the sound source, etc.

The second parameter s₀ is related to the slope of the initial part ofthe streamer 52 relative to a horizontal line 64. The angle s₀ isillustrated in FIG. 3 and it is determined by a tangent T to an initialpart of the streamer and the horizontal line 64. It is noted that theslope of the curved profile at point 54 a is given by a ratio of thechange of the curved profile along the Z axis with respect to the changealong the X axis. The slope is thus equal to the mathematical value ofthe tangent of the angle s₀, i.e., slope (at point 54 a in FIG. 3)=tan(s₀). Further, it is noted that for small angles (e.g., five or lessdegrees), tan (s₀) is approximately equal to s₀, if the angle isexpressed in radians and not in degrees. Thus, for small angles, theslope and the angle may be used interchangeably. In one embodiment, thevalue of s₀ may be between 0 and 6 degrees. The example shown in FIG. 3has an initial angle s₀ equal to substantially 3 degrees. It is notedthat the profile of the streamer 52 in FIG. 3 is not drawn to scale asan angle of 3 degrees is a relatively small quantity.

The third parameter h_(c) indicates a horizontal length (distance alongthe X axis in FIG. 3 measured from the first detector 54 a) of thecurved portion of the streamer. This parameter may be in the range ofhundreds to thousands of meters. For example, h_(c) is around 3000 m forthe configuration shown in FIG. 3. This parameter defines the end of thecurved part of the streamer 52. In other words, the streamer 52 may havea first portion 52 a that has a first curved profile and a secondportion 52 b that is either flat or has a different curved profile.Parameter h_(c) defines the first portion 52 a. It is noted that in oneapplication the streamer 52 has both the first portion 52 a and thesecond portion 52 b while in another application the streamer 52 hasonly the first portion 52 a. In other words, in some embodiments, thestreamer does not extend along the entire curved profile, i.e., a lengthof the streamer projected on X axis is less than h_(c).

According to another exemplary embodiment, the curved profile of thestreamer 52 may be described, approximately, by the following equations:

$\begin{matrix}{{{z(h)} = {{z_{0} + {s_{0}{h\left( {1 - {0.5\left( \frac{h}{h_{c}} \right)}} \right)}\mspace{14mu}{for}\mspace{14mu} h}} \leq h_{c}}},{and}} & (1) \\{{z(h)} = {{z_{0} + {{s_{0} \cdot 0.5 \cdot h_{c}}\mspace{14mu}{for}\mspace{14mu} h}} > {h_{c}.}}} & (2)\end{matrix}$

In these equations, z is measured along the Z axis and h is measuredalong the X axis, where Z is perpendicular to the surface of the waterand X extends along the surface of the water. Also, it is noted thatonly equation (1) may be enough to define the shape of the streamer,depending on the length of the streamer. In other words, in someembodiments, the streamer does not have to have the flat portion. Forthese specific equations, it was found that the clarity of the images ofthe sub-surface improve substantially. Those skilled in the art wouldunderstand that the values provided by equations (1) and (2) areapproximate as the detectors 70 are under constant motion exerted byvarious water currents and the movement of the vessel. In other words,it is understood that detectors that are provided substantially on thecurved profile described by equation (1) and/or (2), e.g., at positionsas close as 10 to 20% to the real curve in terms of the actual depthz(h), are envisioned to be covered by the above mentioned equations. Thesame is true for birds 72 that are configured to maintain the curvedprofile. The curved profile may be one of a parabola, a circle, ahyperbola or a combination of these shapes.

Although the curved profile streamer discussed above provides betterresults than the existing streamer profiles, the processing discussed inthe following exemplary embodiments equally applies to the traditionalstreamer profiles (e.g., horizontal, slanted).

Prior to discussing the novel deghosting process, providing a fewdefinitions and concepts related to seismic data processing is believedto be in order. For this purpose, FIG. 4 illustrates an acquisition setup to be used as an example. As discussed later, another set up may beused.

FIG. 4 illustrates a vessel 84 having an acoustic source 86 and towing astreamer 88. The streamer 88 includes plural detectors 90 and thedetectors are distributed, in this exemplary embodiment, on a slantedstreamer. The incident waves 80 reach the bottom 92 of the ocean, wherepart of them are reflected. However, part of the incident waves continueto travel into the subsurface (structure under bottom 92) where it isreflected by various reflectors 94. At this point, a reflected wave 82starts to propagate towards the surface 96 of the water. This reflectedwave 82 travelling upwards is recorded by detectors 90. However, thereflected wave 82 further travels to the surface 96, where it isreflected by the surface of the water, thus forming the ghosts 98, whichalso are recorded by the detectors 90.

The incident wave 80 (i.e., the wave emitted by the source 86) isassumed to be down-travelling and described by a mathematical functionD. This incident wave D(x, y, z, t) depends on the position (x, y, z)and time t at any point in space. The incident wave D(x, y, z, t) issynthesized recursively at depth z during the migration process. Thedown-travelling wave is being initialized at a depth of the seismicsource z_(s). Considering that there are n detectors, with n from 1 toN, where N is a natural number, the incident wave D at every depth nΔzis then calculated recursively by calculating the incident wave D(x, y,z+Δz, t) at a depth z+Δz from the incident wave D(x, y, z, t) at depthz. This is performed until all the detectors of the streamer are takeninto account.

Similarly, the reflected wave 82, which is described by a mathematicalfunction U(x, y, z, t), is assumed to be up-travelling and it isinitialized at a depth z=z_(r), where z_(r) is a depth of the detectorsif all the detectors have the same depth. If the detectors aredistributed on a slanted streamer or a streamer having a curved profile,the function U needs to be adjusted for each detector as discussedlater. The reflected wave U in an entire volume is then calculatedrecursively by calculating the up-travelling wave U(x, y, z+Δz, t) at adepth z+Δz from the up-travelling wave U(x, y, z, t) at a depth z.

The depths of the detectors, i.e., the fact that the source and thedetectors may have non-zero depths relative to each other may be takeninto account by adding the sources and the detectors at a correspondingz throughout the recursive calculations. For example, a detectorprovided at a depth z_(r), lying between nΔz and (n+1)Δz is added duringthe recursive calculation of U((n+1)Δz) from U(nΔz).

In the case of a mirror migration, the surface of the water is used as amirror: instead of “looking” toward the sea bottom, one “looks” towardthe surface of the water to see the reflectors located below the seismicreceivers. The mirror migration is described in French filed patentapplication serial no. FR1050278, having the title “Method to ProcessMarine Seismic Data”, and U.S. Provisional Patent Application No.61/393,008, entitled Method and Device for Processing Seismic Data, theentire content of which are incorporated herein by reference. The sameapplications also describe a matched mirror migration.

Once the migration is carried out, an image d(x, y, z) is obtained thatincludes residual ghost waves. If the image is obtained by using thematched mirror migration method, the residual ghosts are symmetric. Theimage d(x, y, z) may be considered to be equal to the reflectivity r(x,y, z) convoluted in z with a residual ghost transfer function g(z) asexpressed by the following equation:d(x,y,z)=g(z)·r(x,y,z).

As the residual ghost transfer function g(z) depends only weakly on aposition (x, y, z), the above relation is valid within a given volume.

The operation of estimating the reflectivity r(x, y, z) from the datad(x, y, z) is called deconvolution. This operation needs an estimate ofthe transfer function g(z). Two processes are known to those skilled inthe art for estimating the transfer function g(z) and calculating thereflectivity r(x, y, z) from data d(x, y, z).

One process is the Zero-phase deconvolution with white reflectivity.This process assumes that g(z) is symmetric in z and that thereflectivity has a white autocorrelation in z (equal to an impulse atz=0). A Fourier transform G(k_(z)) of g(z) is real, and a Fouriertransform R(x, y, k_(z)) of r(x, y, z) is complex with modulus 1. Fromhere, it can be derived that G(k_(z)) is the modulus of D(x, y, k_(z)),the Fourier transform in z of d(x, y, z).

The other process is the Minimum-phase deconvolution with whitereflectivity. This process assumes that g(z) is a minimum-phase and thatthe reflectivity has a white autocorrelation in z.

The zero-phase deconvolution makes possible the deconvolution of thematched mirror migration (because in that case g(z) is symmetrical) andthe minimum-phase deconvolution allows the deconvolution of the standardmigration, because for the migration process the residual ghost transferfunction is causal and can be considered minimum-phase. Independent ofwhich of the two procedures is used for obtaining the reflectivity(migration followed by minimum-phase deconvolution or matched mirrormigration followed by zero-phase deconvolution), the assumption of whitereflectivity is necessary for the traditional processes. This assumptionwas commonly used in seismic processing, but is used less and lessbecause the so-called preserved-amplitude processing is becoming moreand more the standard. In this type of processing, it is not only theposition of the reflectors that is of interest, but also theiramplitude, and in this context the assumption of white reflectivitycannot be used.

According to an exemplary embodiment illustrated in FIG. 5, a novelprocessing method does not require the assumption of white reflectivityand preserves the amplitude. In step 500, data acquired, for example,with the set up shown in FIG. 4, is input to a processing apparatus. Instep 502, the migration process is applied to the input data forgenerating, in step 504, an image d₁. Similarly, the same data from step500 may be processed with a mirror migration procedure in step 506 togenerate in step 508 an image d₂. In one application, no deghosting isapplied to the input data of step 500 before steps 504 and 508. Theimage d₁(x, y, z) is obtained by migration (where a recording of eachreceiver is inserted at their true position (x_(r), y_(r), z_(r))) andthe image d₂(x, y, z) is obtained by mirror migration (where a recordingof each receiver is inserted with a change of sign only at thereceiver's mirror position (x_(r), y_(r), −z_(r))).

The migration aligns the primary events so that a coherent summation ofthe primary events is possible and it is shown in FIG. 6. The migrationmakes the ghost events to correspond to z positions (on the Z axis inFIG. 4) greater than the corresponding primary events. This isillustrated in FIG. 6 by the white areas 600 following each line 602.Therefore, the image d₁(x, y, z) includes residual ghost waves which arerepresented by a causal, minimum phase transfer function g_(min)(z),which contaminates by convolution the reflectivity r(x, y, z) as shownin equation (3):d ₁(x,y,z)=g _(min)(z)·r(x,y,z).  (3)The minimum phase transfer function g_(min)(z) is a causal function andits inverse is also causal.

The mirror migration aligns the ghost events by changing their sign tomake their polarity correspond to that of the primary events. Then, acoherent summation of the ghost events is possible and it is shown inFIG. 7. The primary events correspond in this case, as shown in FIG. 7,to z positions smaller than the corresponding ghost events. FIG. 7 showsthe white areas 600 being distributed above (on the Z axis) the lines602. The image d₂(x, y, z) includes residual ghost waves which arerepresented by an anticausal, maximum phase transfer functiong_(max)(z), which contaminates by convolution the reflectivity r(x, y,z) as shown in equation (4):d ₂(x,y,z)=g _(max)(z)*r(x,y,z)  (4)The maximum phase transfer function is an anticausal function and itsinverse is also anticausal.

In other words, the migration stacks coherently the primary events, theghosts events being imperfectly stacked in such a way that the migrationhas a residual ghost wavelet that is causal. The mirror migration stackscoherently the ghosts events with their polarity reversed, in such a waythat the mirror migration has a residual ghost wavelet that isanticausal. In an exemplary embodiment, the deghosting methodillustrated in FIG. 5 uses a “binocular view” of two images (d₁ and d₂)of the same reflectivity r with a different viewpoint to extract a trueamplitude deghosted migration that would have been obtained by aconventional migration if the water-surface was non-reflective.

After calculating d₁(x, y, z) and d₂(x, y, z) by migration and mirrormigration in steps 504 and 508, respectively, the reflectivity r(x, y,z) may be obtained by a “joint deconvolution” procedure performed instep 510 (see FIG. 5). Joint deconvolution refers to a calculationprocedure allowing the reflectivity r(x, y, z), a causal operatorg_(min)(z), and an anticausal operator g_(max)(z) to be obtained fromimages d₁(x, y, z) and d₂(x, y, z) in such a way that equations (3) and(4) are satisfied, exactly or approximately, within a certaincomputational volume V. More specifically, the causal operatorg_(min)(z) is a minimum phase operator, and the anticausal operatorg_(max)(z) is a maximum phase operator. A minimum phase operator or amaximum phase operator are known in control theory. For example, theminimum phase operator has the property that it is causal and stable andits inverse is causal and stable. The maximum phase operator is causaland stable and its inverse is causal and unstable. After the jointdeconvolution step 510, a final image “d” of the subsurface is generatedin step 512. The final image d is illustrated in FIG. 8 and it can beseen that white areas 600 are greatly reduced relative to FIGS. 6 and 7that use the conventional approach.

According to an exemplary embodiment illustrated in FIG. 9, a jointdeconvolution procedure includes a step 900 of defining a volumeV=[x_(min), x_(max)]×[y_(min), y_(max)]×[z_(min), z_(max)] and a step902 of defining a length Dz which depends on a maximum separationbetween an event and its ghost. Further, the procedure includes a step904 of calculating g_(min)(z), g_(max)(z) and r(x, y, z) by consideringthat r is being defined on volume V, g_(min)(z) on the interval [0, Dz]with a normalization g_(min)(z=0)=1, g_(max)(z) on the interval [−Dz, 0]with a normalization g_(max)(z=0)=1. The calculating step 904 isachieved by minimizing a cost function C defined by:C=Σ _((x,y,z)εV){[d ₁(x,y,z)−g _(min)(z)*r(x,y,z)]²+[d ₂(x,y,z)−g_(max)(z)*r(x,y,z)]²}.

The reflectivity r(x, y, z) is being calculated over an entire volume ofinterest by juxtaposing the r(x, y, z) calculated on volume V with anoverlapping zone. It is also possible to use the characteristics of theminimum phase of g_(min)(z) and the maximum phase of g_(max)(z). Basedon the calculated r, a final image is generated in step 906.

Another exemplary embodiment includes replacing the functions g_(min)(z)and g_(max)(z) that depend only on “z” with three-dimensional functionsg_(min)(x, y, z) and g_(max)(x, y, z) which are causal in z andanticausal in z, respectively. In addition, the one dimensionconvolution in z may be replaced by a three dimension convolution. Thisembodiment makes it possible to take into account the dependence of theresidual ghosts of the waves' angles of propagation.

In still another exemplary embodiment, which also makes it possible totake into account the dependence of the residual ghosts on the angles ofpropagation, a transform called a (τ, p_(x), p_(y)) transform is appliedto d₁(x, y, z) and d₂(x, y, z), which transforms the data d₁(x, y, z)into D₁(p_(x), p_(y), τ) and the data d₂(x, y, z) into D₂(p_(x), p_(y),τ). A definition of the (τ, p_(x), p_(y)) transform, also called “slantstack,” can be found, for example, in Seismic Data Processing, OzdoganYilmaz, Society of Exploration Geophysicists 1987, chapter 7, page 429,or in U.S. Pat. No. 6,574,567, the entire content of which areincorporated herein by reference.

Next, for all values (p_(x), p_(y)), the residual ghosts G_(min)(p_(x),p_(y))(τ) and G_(max)(p_(x), p_(y))(τ) are calculated assuming to berespectively causal and anticausal in τ, minimum and maximum phase in τ,and a reflectivity R(p_(x), p_(y), τ) such that:C(p _(x) ,p _(y))=Σ{[D ₁(p _(x) ,p _(y),τ)−G _(min)(p _(x) ,p_(y))(τ)*R(p _(x) ,p _(y),τ)]²+[D ₂(p _(x) ,p _(y),τ)−G _(max)(p _(x) ,p_(y))(τ)*R(p _(x) ,p _(y),τ)]²}is a minimum for all (p_(x), p_(y)), the “*” operation being in thiscase a convolution in τ. The deghosted image, i.e., the reflectivityr(x, y, z), is obtained by calculating the inverse of R(p_(x), p_(y), τ)with the transformation (τ, p_(x), p_(y)).

In the above description, the migrations used are depth migrations forthe images d₁(x, y, z) and d₂(x, y, z). The joint deconvolutionprocedure can also be used with images resulting from time migrations.In the case of a time migration, the image d(x, y, τ) has a temporalparameter τ replacing the depth parameter z. For the time migration, avelocity model v₁(x, y, τ) is used for performing the coherent summationof the primary events. The equivalent for a time mirror migrationprocessing is a migration where, after changing the polarity of theinput data, a velocity v₂(x, y, τ) is used for performing a coherentsummation of the ghost events. Then, a joint deconvolution can beapplied to calculate the final image of the subsurface and the jointdeconvolution is described by:d ₁(x,y,τ)=g _(min)(τ)*r(x,y,τ) and d ₂(x,y,τ)=g _(max)(τ)*r(x,y,τ).

The joint deconvolution step may be generalized to deconvolve more thantwo sets of data, particularly in the case where the receivers are ofdifferent types. For example, if pressure-sensitive receivers such ashydrophones and geophone receivers are used together on the samestreamer or on different streamers, a more complex deconvolution isnecessary for obtaining the final image. For example, assume that theresult of the migration is d₁(x, y, z) and the result of the mirrormigration is d₂(x, y, z) for hydrophone type receivers and the result ofthe migration is d₃(x, y, z) and the result of the mirror migration isd₄(x, y, z) for geophones. The mirror migration of geophone data isachieved by inserting the recordings of each receiver (geophone) attheir mirror positions (x_(r), y_(r), −z_(r)) but without changing thesign for a vertical geophone and with a changed sign for a horizontalgeophone receiver.

Joint deconvolution with four inputs is obtained by modeling themigrations and mirror migrations with the following equations:d ₁(x,y,z)=g ^(h) _(min)(z)*r(x,y,z);d ₂(x,y,z)=g ^(h) _(max)(z)*r(x,y,z);d ₃(x,y,z)=g ^(g) _(min)(z)*c(z)*r(x,y,z); andd ₄(x,y,z)=g ^(g) _(max)(z)*c(z)*r(x,y,z).

Then, by using a least squares type cost function, the causal andminimum phase operators g^(h) _(min)(z) and g^(g) _(min)(z), theanticausal and maximum phase operators g^(h) _(max)(z) and g^(g)_(max)(z), the calibration operator c(z) as well as the reflectivityr(x, y, z) may be determined from the migrations and mirror migrationsimages d₁(x, y, z), d₂(x, y, z), d₃(x, y, z) and d₄(x, y, z).

The cost function can be weighted so as to take into account thedifferent noise spectra of the hydrophone sensors and the geophonesensors. For example, in time migration, the cost function to beminimized is written in the f domain, the Fourier transform of τ:C=Σ{[d ₁(x,y,f)−g ^(h) _(min)(f)·r(x,y,f)]² /B ^(h)(f)+[d ₂(x,y,f)−g^(h) _(max)(f)·r(x,y,f)]² /B ^(h)(f)}·{[d ₃(x,y,f)−g ^(g)_(min)(f)·c(f)·r(x,y,f)]² /B ^(g)(f)+[d ₄(x,y,f)−g ^(g)_(max)(f)·c(f)·r(x,y,f)]² /B ^(g)(f)},where B^(h)(f) and B^(g)(f) are estimates of the power spectra of thehydrophone and geophone noise, respectively.

The procedures described above are not limited to the processing of dataacquired using linear streamers with a constant slope as shown inFIG. 1. The above discussed procedures are also applicable to dataacquired using streamers each having several sections with differentslopes, or streamers having one or more sloped sections and one or morehorizontal sections, or horizontal streamers located at different depthsor streamers having a curved profile.

The above discussed procedures and methods may be implemented in aprocessing apparatus illustrated in FIG. 10. Hardware, firmware,software or a combination thereof may be used to perform the varioussteps and operations described herein. The processing apparatus 1000 ofFIG. 10 is an exemplary computing structure that may be used inconnection with such a system.

The exemplary processing apparatus 1000 suitable for performing theactivities described in the exemplary embodiments may include a server1001. Such a server 1001 may include a central processor (CPU) 1002coupled to a random access memory (RAM) 1004 and to a read-only memory(ROM) 1006. The ROM 1006 may also be other types of storage media tostore programs, such as programmable ROM (PROM), erasable PROM (EPROM),etc. The processor 1002 may communicate with other internal and externalcomponents through input/output (I/O) circuitry 1008 and bussing 1010,to provide control signals and the like. The processor 1002 carries outa variety of functions as is known in the art, as dictated by softwareand/or firmware instructions.

The server 1001 may also include one or more data storage devices,including hard and floppy disk drives 1012, CD-ROM drives 1014, andother hardware capable of reading and/or storing information such asDVD, etc. In one embodiment, software for carrying out the abovediscussed steps may be stored and distributed on a CD-ROM 1016, diskette1018 or other form of media capable of portably storing information.These storage media may be inserted into, and read by, devices such asthe CD-ROM drive 1014, the disk drive 1012, etc. The server 1001 may becoupled to a display 1020, which may be any type of known display orpresentation screen, such as LCD displays, plasma display, cathode raytubes (CRT), etc. A user input interface 1022 is provided, including oneor more user interface mechanisms such as a mouse, keyboard, microphone,touch pad, touch screen, voice-recognition system, etc.

The server 1001 may be coupled to other devices, such as sources,detectors, etc. The server may be part of a larger network configurationas in a global area network (GAN) such as the Internet 1028, whichallows ultimate connection to the various landline and/or mobilecomputing devices.

According to an exemplary embodiment illustrated in FIG. 11, there is amethod for deghosting seismic data related to a subsurface of a body ofwater. The method includes a step 1100 of inputting data recorded bydetectors that are towed by a vessel, the data being associated withwaves travelling from the subsurface to the detectors; a step 1102 ofapplying a migration procedure to the data to determine a first image ofthe subsurface; a step 1104 of applying a mirror migration procedure tothe data to determine a second image of the subsurface; a step 1106 ofjoint deconvoluting the first image and the second image for deghostinga reflectivity of the subsurface; and a step 1108 of generating a finalimage of the subsurface based on the deghosted reflectivity of the jointdeconvoluting step.

The disclosed exemplary embodiments provide an apparatus and a methodfor seismic data processing. It should be understood that thisdescription is not intended to limit the invention. On the contrary, theexemplary embodiments are intended to cover alternatives, modificationsand equivalents, which are included in the spirit and scope of theinvention as defined by the appended claims. Further, in the detaileddescription of the exemplary embodiments, numerous specific details areset forth in order to provide a comprehensive understanding of theclaimed invention. However, one skilled in the art would understand thatvarious embodiments may be practiced without such specific details.

Although the features and elements of the present exemplary embodimentsare described in the embodiments in particular combinations, eachfeature or element can be used alone without the other features andelements of the embodiments or in various combinations with or withoutother features and elements disclosed herein.

This written description uses examples of the subject matter disclosedto enable any person skilled in the art to practice the same, includingmaking and using any devices or systems and performing any incorporatedmethods. The patentable scope of the subject matter is defined by theclaims, and may include other examples that occur to those skilled inthe art. Such other examples are intended to be within the scope of theclaims.

What is claimed is:
 1. A method for deghosting seismic data related to asubsurface of a body of water, the method comprising: receiving datarecorded with seismic detectors distributed along a streamer, the databeing associated with waves travelling from the subsurface to theseismic detectors; applying with a processing apparatus a migrationprocedure to the data to determine a first dataset indicative of thesubsurface; applying with the processing apparatus a mirror migrationprocedure to the data to determine a second dataset indicative of thesubsurface; joint deconvoluting with the processing apparatus the firstdataset and the second dataset for deghosting a reflectivity of thesubsurface; and generating with the processing apparatus an image of thesubsurface based on the deghosted reflectivity of the jointdeconvoluting step.
 2. The method of claim 1, wherein the deghosting isperformed during an imaging phase and not in a preprocessing phase witha processing apparatus.
 3. The method of claim 1, wherein no datumingstep is performed on the data.
 4. The method of claim 1, wherein atravelling angle of the waves propagating from the subsurface to thedetectors or from a surface of the water to the detectors is notrestricted.
 5. The method of claim 1, wherein the data is threedimensional data and the migration, the mirror migration and the jointdeconvolution are three dimensional procedures.
 6. The method of claim1, wherein the data are collected from streamers having birds that arecontrolled to achieve a curved profile.
 7. The method of claim 1,wherein the migration procedure comprises: recursively synthesizing anincident wave D(x, y, z+Δz, t) at a depth z+Δz from a previous incidentwave D(x, y, z, t) at depth z.
 8. The method of claim 1, wherein themirror migration procedure comprises: recursively synthesizing anup-travelling wave U(x, y, z+Δz, t) at a depth z+Δz from a previousup-travelling wave U(x, y, z, t) at a depth z.
 9. The method of claim 1,wherein the joint deconvoluting comprises: determining the reflectivityr(x, y, z), a minimum phase transfer function g_(min)(z), and a maximumphase transfer function g_(max)(z) based on equations:d ₁(x,y,z)=g _(min)(z)*r(x,y,z), andd ₂(x,y,z)=g _(max)(z)*r(x,y,z), wherein z is a depth of a pointrelative to the surface of the water, and x and y are coordinates of thepoint in a plane substantially parallel with the surface of the water.10. The method of claim 9, wherein the g_(min)(z) and g_(max)(z) arethree dimensional functions.
 11. The method of claim 1, wherein themigration is a depth migration.
 12. The method of claim 1, wherein themigration is a time migration.
 13. The method of claim 1, wherein thejoint deconvolution comprises: calculating a cost function C fordetermining the reflectivity, wherein the cost function C is given by:C=Σ _((x,y,z)εV){[d ₁(x,y,z)−g _(min)(z)*r(x,y,z)]²+[d ₂(x,y,z)−g_(max)(z)*r(x,y,z)]²}, where d₁(x, y, z) is the first dataset, d₂(x, y,z) is the second dataset, g_(min)(z) is a minimum phase transferfunction, g_(max)(z) is a maximum phase transfer function, z is a depthof a point relative to the surface of the water, x and y are coordinatesof the point in a plane substantially parallel with the surface of thewater, and V is a predetermined volume.
 14. The method of claim 1,further comprising: applying a (τ, p_(x), p_(y)) transform to the firstdataset d₁(x, y, z) and the second dataset d₂(x, y, z), to transform thefirst dataset d₁(x, y, z) into D₁(p_(x), p_(y), τ) and the seconddataset d₂(x, y, z) into D₁(p_(x), p_(y), τ).
 15. The method of claim 1,wherein the data includes recordings from hydrophones and geophones. 16.The method of claim 15, wherein a result of the migration procedure isd₁(x, y, z) and a result of the mirror migration procedure is d₂(x, y,z) for hydrophone type receivers and a result of the migration procedureis d₃(x, y, z) and a result of the mirror migration procedure is d₄(x,y, z) for geophones.
 17. The method of claim 16, further comprising:generating the image using a joint deconvolution of d₁(x, y, z), d₂(x,y, z), d₃(x, y, z), and d₄(x, y, z) and based on the followingequations:d ₁(x,y,z)=g ^(h) _(min)(z)*r(x,y,z);d ₂(x,y,z)=g ^(h) _(max)(z)*r(x,y,z);d ₃(x,y,z)=g ^(g) _(min)(z)*c(z)*r(x,y,z); andd ₄(x,y,z)=g ^(g) _(max)(z)*c(z)*r(x,y,z), where g^(h) _(min) and g^(g)_(min) are minimum phase transfer functions, g^(h) _(max)(z) and g^(g)_(max)(z) are maximum phase transfer functions, z is a depth of a pointrelative to the surface of the water, x and y are coordinates of thepoint in a plane substantially parallel with the surface of the water,and c(z) is a calibration operator.
 18. A processing device fordeghosting seismic data related to a subsurface of a body of water, theprocessing device comprising: an interface configured to receive datarecorded by detectors that are distributed along a streamer, the databeing associated with waves travelling from the subsurface to thedetectors; and a processor connected to the interface and configured to,apply a migration procedure to the data to determine a first datasetrepresentative of the subsurface, apply a mirror migration procedure tothe data to determine a second dataset representative of the subsurface,joint deconvolute the first dataset and the second dataset fordeghosting a reflectivity of the subsurface, and generate an image ofthe subsurface based on the deghosted reflectivity of the jointdeconvoluting step.
 19. The processing device of claim 18, wherein theprocessor is configured to deghost the image during an imaging phase andnot in a preprocessing phase.
 20. A non-transitory computer readablemedium including computer executable instructions, wherein theinstructions, when executed, implement a method for deghosting seismicdata related to a subsurface of a body of water, the method comprising:inputting data recorded by detectors that are distributed along astreamer, the data being associated with waves travelling from thesubsurface to the detectors; applying a migration procedure to the datato determine a first dataset representative of the subsurface; applyinga mirror migration procedure to the data to determine a second datasetrepresentative of the subsurface; joint deconvoluting the first datasetand the second dataset for deghosting a reflectivity of the subsurface;and generating an image of the subsurface based on the deghostedreflectivity of the joint deconvoluting step.